A Cantor set in the plane and its monotone subsets

DOI10.1007/s10474-015-0569-7zbMath1374.54034OpenAlexW2266212720MaRDI QIDQ519942

Aleš Nekvinda

Publication date: 31 March 2017

Published in: Acta Mathematica Hungarica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10474-015-0569-7

zbMATH Keywords

Cantor setHausdorff dimensionHausdorff measuremonotone metric space

Mathematics Subject Classification ID

Linearly ordered topological spaces, generalized ordered spaces, and partially ordered spaces (54F05) Fractals (28A80) Hausdorff and packing measures (28A78)

Cites Work

• Unnamed Item
• Monotone metric spaces
• Ultrametric subsets with large Hausdorff dimension
• Some results on monotone metric spaces
• Properties of functions with monotone graphs
• Hausdorff Dimension of Metric Spaces and Lipschitz Maps onto Cubes
• Universal measure zero, large Hausdorff dimension, and nearly Lipschitz maps
• A Cantor set in the plane that is not σ-monotone
• Self-similar sets in complete metric spaces
• Cardinal invariants of monotone and porous sets

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